It would be epic to be able to ride on certain pokemon (e.g. Arcanine and Tauros, but not things that aren't able to have a passenger, like drifbloom and hoppip) and have their Pokéathlon speed stat determine how fast they would go.
EDIT; While i was thinking about this: Why not make a Ride HM which would replace the bike?

Riding on Pokemon and a HM to do that would just be... creepy. XD If the feature was to return I think it'd stick to just Pokemon following you or else you might get a re-appearance of N yelling at you :x